Shape space exploration of constrained meshes

Yongliang Yang, Yijun Yang, Helmut Pottmann, Niloy J. Mitra

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We present a general computational framework to locally characterize any shape space of meshes implicitly prescribed by a collection of non-linear constraints. We computationally access such manifolds, typically of high dimension and co-dimension, through first and second order approximants, namely tangent spaces and quadratically parameterized osculant surfaces. Exploration and navigation of desirable subspaces of the shape space with regard to application specific quality measures are enabled using approximants that are intrinsic to the underlying manifold and directly computable in the parameter space of the osculant surface. We demonstrate our framework on shape spaces of planar quad (PQ) meshes, where each mesh face is constrained to be (nearly) planar, and circular meshes, where each face has a circumcircle. We evaluate our framework for navigation and design exploration on a variety of inputs, while keeping context specific properties such as fairness, proximity to a reference surface, etc.
Original languageEnglish (US)
Title of host publicationProceedings of the 2011 SIGGRAPH Asia Conference on - SA '11
PublisherAssociation for Computing Machinery (ACM)
ISBN (Print)9781450308076
StatePublished - 2011
EventSIGGRAPH Asia 2011 - Hong Kong,China
Duration: Jan 1 2011 → …


ConferenceSIGGRAPH Asia 2011
Period01/1/11 → …

Bibliographical note

KAUST Repository Item: Exported on 2017-06-20


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